Ok, I'm genuinely confused. There's two interesting things about this from Raghuram Rajan's Financial Times editorial, Sensible Keynesians see no easy way out, that we should unpack (my bold and numbering):

The key question then is whether more government spending can make a real difference to the most severe employment problems. Here the case for a general stimulus becomes less compelling. [1]In the US, demand is weakest in communities where a boom and bust in house prices has left an overhang of household debt. Lower local demand has hit employment in industries such as retail and restaurants. A general increase in government spending may be too blunt – greater demand in New York is not going to help families eat out in Las Vegas (and hence create more restaurant jobs there). [2] Targeted household debt write-offs in Las Vegas could be a better use of stimulus dollars....

Targeted government spending, or reduced austerity, along the lines suggested by sensible Keynesians, might be feasible in some countries and helpful in speeding recovery. But we should examine each policy based on a country’s circumstances. We should be particularly wary of populist Keynesians, who parrot “in the long run we are dead” to justify any short-sighted government action. They do the world a disservice by suggesting there are easy ways out.

So Rajan is a sensible Keynesian who would push us towards targeted, household mortgage-debt write-offs. Meanwhile others, including presumably Paul Krugman, are a dangerous, populist variety of Keynesian who want fiscal or monetary stimulus.

The first numbered argument is true - places where housing prices collapsed the most are hardest hit by unemployment. But unemployment is still a nation-wide phenomenon, hitting places that didn't even have a housing bubble. Let's chart the ratio of unemployment for April 2012 versus the unemployment for December 2007 state-by-state (source, click for larger image):

The average increase is 1.65. In New York, which Rajan singles out as being ok, unemployment has gone from 4.7 percent to 8.5 percent, which gives us an above-the-average ratio of 1.8. This is not a localized crisis.

Now Rajan is almost certainly alluding to a graph like this, which we put together a year and a half ago (sigh), of unemployment against the percentage of homes that are deeply underwater, or more than 50% underwater:

There's a lot of ways to visulize this relationship between housing bust and unemployment - Jared Bernstein had one recently. But let's examine this relationship in light of Rajan's suggestion that "Targeted household debt write-offs" could be "a better use of stimulus dollars."

There's three stories explaining this this relationship between unemployment and underwater housing. The first is a structural story. Can't turn housing construction workers into nurses, underwater homeowners can't move, etc. The mobility story turns out to be incorrect, and the "skills" story has problems we've discussed elsewhere. But notice that writing down mortgage debt doesn't make a construction worker into a nurse. So writing down mortgage debt doesn't help with this story.

There's a second story about this graph that describes a "wealth effect." People where housing values collapsed feel poorer, so they spend less. The latest Economic Report of the President argued that the "severity of losses experienced during the recession that began in December of 2007 in both national output and in labor markets makes these [wealth-effect] estimates appear too small." Also households are the net seller, but also net buyer, of housing - it's not clear, outside demographics, that housing shifts should make the macroeconomy feel poorer. But either way, writing down mortgage debt would not help with the wealth effect: if all the housing was paid in cash we'd still have the same recession under this second story.

Now there's a third story, a "balance-sheet" story of the recession. Here consumers are overleveraged and are cutting back on consumption until their balance-sheet, or their amount of debt, is repaired. In this story, reducing household mortgage debt can be a really great use of stimulus dollars. We walked through this story in this interview with Amir Sufi, who has done the leading empirical work on this. And the key, recent, theorectical work on this story, the best model of how this happens, was done by.....Paul Krugman. Specifically Eggertsson/Krugman's "Debt, Deleveraging, and the Liquidity Trap."

If the problem is household's balance-sheets, you can either make people richer or reduce their debts. Rajan thinks that taking money and writing down debt is a good idea. You could also take that money, give it to people in exchange for building useful public stuff; they can pay down debts, and then everyone has some stuff that helps the productive capabilities of the economy. You could also just give people money by not collecting taxes and mailing out checks, and they can efficiently choose whether or not to reduce debts. But under the three most common stories for the relationship between housing and debt, Rajan's policy recommendation only makes sense in the context of deleveraging, or a serious demand story, or the theory that is animating the so-called "populist" Keynesian wing.

This debate is frustratingly not new. Christina Romer was telling media in early 2009 that balance-sheet problems become worse if you let unemployment soar, even if you reduce debts. Romer: "Actually, you know, a crucial thing–when [FDR] did the bank holiday, it took the next two years to actually clean up the banks, that we actually did not get the things really cleaned up until 1935. And that a big part of that cleanup was he managed to turn around the real economy. We saw employment growing again, GDP growing again, and that inherently helps your financial system." Nothing messes up balance-sheets like mass unemployment and falling median wages.

As we've seen, writing down mortgage debt is a viciously ugly, difficult, zero-sum battle. I think it makes good sense to consider, and will have some more formal writing on it, but the idea that it is the sensible ideal while everyone else pushing fiscal or monetary stimulus is behaving irresponsibly is wrong - they both are working from the same intellectual framework.